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Topic: The Reality Equation (Read 17892 times) |
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David Lucifer
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Re:The Reality Equation
« Reply #15 on: 2012-03-10 21:51:27 » |
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Removing the extraneous bits meant for human consumption, the metaverse program reduces to just this:
def f(X):
f(X + "0")
f(X + "1")
f("")
Incredibly simple, yet it generates infinite complexity?
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Blunderov
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Re:The Reality Equation
« Reply #16 on: 2012-03-12 17:21:23 » |
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[Blunderov] That's a big number. Here are some more big numbers.
Listverse
10 Enormous Numbers
12/03/2012 J Frater
One of the first questions that kids often ask is “What is the biggest number?” This question is an important step in transitioning to a world of abstract concepts. The answer is of course that numbers are generally considered endless, but there gets to be a point were numbers become so big that there really is no point in having them, they have no real importance outside of the fact that yes technically they do exist. To make a list like this I could simply write down a massive number for the first number, and then write +1, +2, +3 and so on for the rest of the list. Instead I chose to take out 10 numbers that do have some effect on the world and place them in ascending order, giving a brief explanation as to what they are and how they have some relevance on the world, albeit very small relevance, especially when compared to the size of the number itself.
10
10^80
Ten to the eightieth power – a 1 with 80 zeros after it – is quite massive but somewhat tangible at least from a relatively concrete point of view. This is the estimated number of fundamental particles in the known universe, and with fundamental particles we’re not talking about microscopic particles, we’re talking about much smaller things like Quarks and Leptons – subatomic particles. The name for this number in U.S. and Modern British is “One Hundred Quinquavigintillion” I would write out phonetically how to pronounce that but I don’t have a clue. The concept of the amount of such small things and how many of them make up the entire universe may seem overwhelming, but it is the smallest and easiest to understand of the numbers on this list.
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One Googol
The word googol, with a slightly different spelling, has become a frequently used verb in modern times, thanks to a highly popular search engine. The number has an interesting history which you can find by simply googling it. The term was coined by Milton Sirotta in 1938 when he was 9 years old. Although this is a relatively abstract number, only existing for the fact that it technically exists, but it does come up occasionally in other uses.
Mental Calculator Alexis Lemaire set a world record for calculating the 13th root of a 100 digit number, the 13th root of 8,192 is 2, or 2 times itself thirteen times, 100 digit numbers are googols, one of the numbers that Lemaire had calculated would have read (3 googol, 893 Duotrigintillion, ext, ext.) Another use is from about 1 to 1.5 googol years after the big bang, the most massive black holes will have exploded. These will be the last recognizable structure of our universe to disintegrate, and once it does the universe will enter its 5th and final era – known as the Dark Era – the end of the universe based on certain scientific models.
8
8.5 x 10^185
A Plank length is extremely small, approximately 1.616199 x 10-35 meters, or in long form 0.00000000000000000000000000000616199 meters. There are about a googol of them in a 1 inch cube. Plank length and Plank volumes are important in quantum physics branches like string theory – evidently sizes this small allow the extra dimensions to be detected, at least in some theories. How do all these small things apply to the third smallest number of this list? There are approximately 8.5 x 10^185 plank volumes in the universe. This number is both massive and its practical purpose relatively non-existent, however it is still simple compared to the rest of the numbers on this list.
7
2^43,112,609 – 1
The third largest number on this list, the number of all the plank volumes in the universe, consists of 185 digits. This number here consists of almost 13 million digits. The significance of this number is that it is currently the largest known prime number. It was discovered in August of 2008 by the Great Internet Messene Prime Search (GIMPS). From here on the numbers become much more difficult to render.
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Googolplex
A lot of people have heard this word as well, fans of the Back to the Future movies may remember Dr. Emit L. Brown muttering the line “she’s one in a million, one in a billion, one in a googolplex.” But what is a googolplex? Remember how long a googol is? A one with a hundred zeros after it, a googolplex is a 1 with a googol zeros after it. How big is this number? If the entire universe was filled with paper and all that those papers had written on them were zeros at a size 10 font, it would only be about half the zeros required to write out this number in the long form. Even writing the number in scientific notation is not very practical, for a number this large it requires yet another type of notation, something called a power tower. For example our first number 10^80 is the first part of a power tower, as the power tower grows the next number would be placed as a superscript above and to the right of the 80. These are not always possible to write in digital text, so we have to use yet another short hand, the same method used on a graphing calculator, the symbol “^”. So item 10 on this list can be rendered as so 10^80, or ten to the eightieth. Now with this form of notation we can more easily write out the googolplex, which is 10^10^100, or ten to the tenth to the one hundredth. We will also be using these towers for the next few numbers so I hope you’re okay with conceptualizing them.
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Skewe’s numbers
Skewe’s Number is the upper bounds to the math problem that π(x) > Li(x), a simple looking enough equation, however Li is a much more complicated equation in it’s own right. Essentially Skewe’s number proves that a number “x” exists that violates this rule, assuming that Reimanns hypothesis is true then that number “x” is less than 10^10^10^36, (most numbers are) the first of Skewe’s Numbers, much bigger than a googolplex, noted because of the extra tower. There is also an even large Skewe number, without assuming Reimanns hypothesis, x is less then 10^10^10^963.
4
Poincare Recurrence Time
This is very complicated stuff, but the core concept is relatively simple: “given enough time, anything is possible” Poincare recurrence time is the amount of time that it would take for the entire universe to return to a state that is relatively the same as to what it is today, caused by random quantum fluctuations, or in more simplified terms, “History will repeat itself.” The high estimate of how long this will take is 10^10^10^10^10^1.1 years.
3
Graham’s Number
This number is massive – in the 1980s it was listed in the Guinness book of world records as the most massive finite number ever used in a serious mathematical proof. It was created Ron Graham, as the upper bounds to a problem in Ramsey Theory involving multicolored hyper cubes. The number is so big even a power tower would be too cumbersome to represent the number. The only way to easily represent the number is to use Knuth’s Up-Arrow Notation and it’s own equation. Let’s go through this piece by piece.
First Knuth’s Up-Arrow Notation is a method of writing very large numbers, it would be much too complicated to explain exactly how the arrows work here, but you can visualize it this way. 3↑3 translates to 33 or 27, 3↑↑3 translates to 3^3^3 or 7,625,597,484,987. Now if you were to add another arrow to the number 3↑↑↑3, then the power tower would be over 7.5 trillion levels. This alone is much much bigger than the Poincare Recurrence time, and you can add an infinite amount of arrows and each arrow makes the number that much more powerful.
The representation of Graham’s number is: G=f64(4), where f(n)=3↑^n3. The best way to look at this is in layers. The first layer is 3↑↑↑↑3, which is already a number too massive to represent in most other forms. The next layer has that many arrows between 3s. Then take that answer and put that many arrows into the next layer between 3s, and this goes on for 64 layers. If you’re interested the last ten digits of Grahams Number are 2464195387, no one, not even Graham himself knows what the first digit is.
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Infinity
Most people know of this number and it is used in hyperbole all the time – kind of like the number one zillion – but it’s more complicated then most people realize, and if you thought the numbers that came before this one were strange, this one is even stranger, and a controversial number too. According to the rules of infinity, there are an infinite number of odd numbers and even numbers in infinity even though there can only be half as many odd numbers as total numbers. Infinity plus one equals infinity, infinity minus one equals infinity, infinity plus infinity equals infinity, infinity divided in half is still infinity, but infinity minus infinity is not exactly understood, infinity divided by infinity would probably be 1.
Scientists estimate 1080 subatomic particles in our known universe, but that is the known universe, or the observable universe. A lot of scientists, however, believe that the universe is infinite, or if they don’t believe this is the case they still accept it as a possibility. If this is the case then by mathematics alone there must be another Earth out there where every atom happens to be in the exact same location in relation to every other atom on Earth as it is in our own. The chances of two carbon copy Earths are extremely small, however in an infinite universe it not only can occur but it has to occur, and not only that, there has to be an infinite amount of carbon copy Earths out there if the universe does in fact go one forever.
Not all people believe in infinity however, Israeli Mathematics Professor Doron Zeilberger, stated that he feels numbers do not go on forever and there is a number so large that when you add 1 to it you will go back to zero, however this number is much higher then anything humans can comprehend, and that number may never be found or proven, this belief is the main pillar in a mathematical philosophy known as Ultrafinitism.
1
Infinity+1 – Infinity + 1
Sorry. I had to do it.
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David Lucifer
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Re:The Reality Equation
« Reply #17 on: 2012-03-17 11:38:43 » |
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Quote from: Blunderov on 2012-03-12 17:21:23
Scientists estimate 1080 subatomic particles in our known universe, but that is the known universe, or the observable universe. A lot of scientists, however, believe that the universe is infinite, or if they don’t believe this is the case they still accept it as a possibility. If this is the case then by mathematics alone there must be another Earth out there where every atom happens to be in the exact same location in relation to every other atom on Earth as it is in our own. The chances of two carbon copy Earths are extremely small, however in an infinite universe it not only can occur but it has to occur, and not only that, there has to be an infinite amount of carbon copy Earths out there if the universe does in fact go one forever.
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I don't understand how an infinite universe implies an infinite number of carbon copy earths. Can anyone enlighten me?
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Blunderov
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Re:The Reality Equation
« Reply #18 on: 2012-03-17 16:38:31 » |
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[Blunderov] Well, my grasp on the subject is very tenuous but this is my take: there seem to be different kinds of infinity. One kind of infinite universe seems to be a two dimensional plane where if some imaginary thing could travel at 16 billion times the speed of light it would eventually land up back in the same place it started - were it not for the fact that the place where it started wouldn't be the same space anymore (one can never step into the same river twice). But it is, so to speak, a bounded infinity in which only a limited number of probabilities could actually occur - although there are boundless possibilities from which to choose.
Another kind of infinite universe would be one that contained every single thing that could possibly happen. Even if some imaginary thing could travel at 16 billion times the speed of light, in such a universe it would always have further to go even if the universe wasn't expanding. It is, so to speak, an unbounded infinity and it would contain an infinite number of identical Earths becuse this would be a possible thing that could happen.
I'm not too sure if such an unboundedly infinite universe would of necessity contain something that is infinitely small. That notion doesn't make sense to me: something would have to be so small as to not exist all, so perhaps it is a category error. But then one does have to wonder why to speak of something as "infinitely big" (in this unbounded sense) isn't also a category error. I rather suspect it is although, I admit, I have no proof.
So, I must resort to Occam's razor and conclude that the bounded infinity is the more convincing candidate but with some reluctance: I rather liked the notion of an infinity of duplicate Earths. It would mean that in a very strange kind of way we would live forever. Oh well.
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Fritz
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Re:The Reality Equation
« Reply #19 on: 2012-03-18 15:58:37 » |
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[Fritz] I suspect I'm being a nuisance again; but away ways .....
So are we in one 'Russian Doll' which is our known universe and the 'Dolls' getting smaller or larger infinitely in either directions. Or; are there endless 'Russian Dolls' of varying form and we are in an infinite sea of them ?
This question occurs to me as a 'Reality Equation' seems to me to beg on the model of an endless rendering (time series) rather then endless variability (space envelope).
I start to go tilt because all the new Quantum Physics research seems to hold for self evident that as Quantum models start explaining themselves in the the macro world the notion of "Space and Time" is demonstrated as 'garble and chaff' of numerous Quantum effects and as such don't exist in the universe except to model the Einstein Universe.
Yet even:
Quote:Posted by: David Lucifer Posted on: 2012-03-10 21:51:27
Removing the extraneous bits meant for human consumption, the metaverse program reduces to just this:
def f(X):
f(X + "0")
f(X + "1")
f("")
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As the equation loops and increments it is still resolved as space in time in a computer realm doing it's calculations. Yet space and time has no application in the modelling the universe according to Quantum theory. If strings and bits can exist simultaneously in different states and in different places, can we model it ?
"As I Quantumfy this in my mind the Gravity starts slipping away" ... groan...
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Where there is the necessary technical skill to move mountains, there is no need for the faith that moves mountains -anon-
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David Lucifer
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Re:The Reality Equation
« Reply #20 on: 2012-03-26 13:40:52 » |
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Quote from: Blunderov on 2012-03-17 16:38:31
Another kind of infinite universe would be one that contained every single thing that could possibly happen. Even if some imaginary thing could travel at 16 billion times the speed of light, in such a universe it would always have further to go even if the universe wasn't expanding. It is, so to speak, an unbounded infinity and it would contain an infinite number of identical Earths becuse this would be a possible thing that could happen.
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I agree that a universe that contained an infinite number of earth copies would necessarily be infinite, but an infinite universe does not necessarily contain an infinite number of earth copies (e.g. a universe that contains 1 earth and an infinite number of Saturn copies). Therefore I conclude an infinite universe does not necessarily imply infinite earths.
I happen to think there are an infinite number of earth copies, but they are in the Metaverse, not an infinite universe. See next message.
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David Lucifer
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Re:The Reality Equation
« Reply #21 on: 2012-03-26 13:50:38 » |
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Quote from: Fritz on 2012-03-18 15:58:37 [Fritz] I suspect I'm being a nuisance again; but away ways .....
So are we in one 'Russian Doll' which is our known universe and the 'Dolls' getting smaller or larger infinitely in either directions. Or; are there endless 'Russian Dolls' of varying form and we are in an infinite sea of them ?
This question occurs to me as a 'Reality Equation' seems to me to beg on the model of an endless rendering (time series) rather then endless variability (space envelope).
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The reality equation generates infinite values (numbers) encoded in bit strings. Time and space are supervenient on this model. I don't know how but time and space are how some numbers (us) interpret their own context.
Quote:I start to go tilt because all the new Quantum Physics research seems to hold for self evident that as Quantum models start explaining themselves in the the macro world the notion of "Space and Time" is demonstrated as 'garble and chaff' of numerous Quantum effects and as such don't exist in the universe except to model the Einstein Universe.
Yet even:
Quote:Posted by: David Lucifer Posted on: 2012-03-10 21:51:27
Removing the extraneous bits meant for human consumption, the metaverse program reduces to just this:
def f(X):
f(X + "0")
f(X + "1")
f("")
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As the equation loops and increments it is still resolved as space in time in a computer realm doing it's calculations. Yet space and time has no application in the modelling the universe according to Quantum theory. If strings and bits can exist simultaneously in different states and in different places, can we model it ?
"As I Quantumfy this in my mind the Gravity starts slipping away" ... groan...
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The algorithm should be imagined to run on the Metaverse computer which is not bound by the time and space limitations of computers in our universe. The Metaverse computer is metaphorical in that it runs infinitely fast and has infinite memory to store all values, so in a sense all variation is generated simultaneously.
One odd implication mentioned in the previous message is that anything that can be encoded in a finite bit string (a song, a book, a person, a planet, our own universe) is instantiated as a substring an infinite number of times. Just add any other bit string to the beginning or end and it forms another bit string that is instantiated in the Metaverse. Therefore infinite Earths.
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David Lucifer
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Re:The Reality Equation
« Reply #22 on: 2013-05-14 14:35:39 » |
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Quote:There is a fastest, optimal, most efficient way of computing all logically possible universes, including ours — if ours is computable (no evidence against this). Any God-like “Great Programmer” with any self-respect should use this optimal method to create and master all logically possible universes.
At any given time, most of the universes computed so far that contain yourself will be due to one of the shortest and fastest programs computing you. This insight allows for making non-trivial predictions about the future. We also obtain formal, mathematical answers to age-old questions of philosophy and theology. |
Transcript of Jürgen Schmidhuber’s TEDx talk at UHasselt, Belgium, Nov. 10, 2012
http://www.kurzweilai.net/in-the-beginning-was-the-code
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Hermit
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Re:The Reality Equation
« Reply #23 on: 2013-05-15 10:02:06 » |
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Excellent reasoning.
From a recent dialog:
X: are you actually here or just pretending?
me: Pretending of course. What makes you think that I exist anymore than the Bishop of Woolwich really exists?
me: Just a non-existent idea in the unlikely imagination of an improbable god... [Refers to: John Robinson (Bishop of Woolwich) whose controversial sixties book, "Honest to God" caused Michael Flanders (of "Drop of a Hat" fame) to suggest that Robinson was "just an idea in the mind of god."]
As once discussed with Lucifer (in the context of the meta-invalidity of the asinine concept of copyright), I don't think that the metaverse requires a computer with infinite storage or speed to represent anything, or indeed, everything. Just a mind capable of conceiving the idea of a closely coupled Turing Machine and noise source.
This is because, if you accept that all possible bit strings can exist and may be made up of recursive self-referential (not necessarily yielding unique hash functions) indices, and thus that anything (and everything) may be encoded by any quantitised noise string (in which all states are encoded with equal potential) of any length capable of representing a hash (and this means that, in its most reduced form, a single bit might e.g. store the parity of a noise string of any length, and thus anything :- , you can reasonably infer that such encoding does exist, has been created (and published by existing noise sources!), but, without the significance necessarily having been recognised (you may need to analyse a lot of noise, the significance of which might evade you, to find the complete works of Shakespeare, but they are out there - an infinite number of times!); and so you may validly regenerate the underlying bit streams at need, as the only reason to bother to instantiate the data would be to search for something within them - and as you have already stipulated that any pattern may be represented by any bitstream, it follows that all searches will yield the result that you are seeking - with the implication that everything, real and imaginary, that can exist, has already been published within existing noise sources.
With acknowledgements to Gödel, Turing and Shannon
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With or without religion, you would have good people doing good things and evil people doing evil things. But for good people to do evil things, that takes religion. - Steven Weinberg, 1999
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David Lucifer
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Re:The Reality Equation
« Reply #24 on: 2016-07-13 19:38:48 » |
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Just came across this image in a reddit thread. In the first post I used the Om symbol to represent reality.
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Fox
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Re:The Reality Equation
« Reply #25 on: 2016-11-30 06:18:30 » |
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Perhaps I should have started a new thread on this instead, but has anyone here seen Thrive, and it's hypocritical implications? The Torus concept they use in the beginning, and it's patterns in nature, reminded me a little of this thread - http://www.thrivemovement.com/the_movie
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I've never expected a miracle. I will get things done myself. - Gatsu
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Fox
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Re:The Reality Equation
« Reply #27 on: 2016-12-06 04:36:52 » |
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Quote from: David Lucifer on 2016-12-01 15:06:40 | UFOs? crop circles? I recommend skepticism. |
Ah, yes, there were extra-terrestrial implications in there as well. I should have noted/warned you of that caveat. Not that I buy into crop circles, but yet neither am I sufficiently qualified to really comment on them all. However, there are some amazingly complex patterns out there which I never actually quite realized until watching that video; which of course, and I completely agree with that a large dose of skepticism is necessary. The patterns in nature and the energy implications surrounding them are also quite interesting, but surely not our only options (if really options at all) for a clean and sustainable environment/world.
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I've never expected a miracle. I will get things done myself. - Gatsu
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David Lucifer
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Re:The Reality Equation
« Reply #28 on: 2021-10-31 10:16:50 » |
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A Computer Scientist's View of Life, the Universe, and Everything
Juergen Schmidhuber
Is the universe computable? If so, it may be much cheaper in terms of information requirements to compute all computable universes instead of just ours. I apply basic concepts of Kolmogorov complexity theory to the set of possible universes, and chat about perceived and true randomness, life, generalization, and learning in a given universe.
https://arxiv.org/abs/quant-ph/9904050
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